School of Mathematics and Physics - UQ eSpace
http://espace.library.uq.edu.au/
The University of QueenslandenFez http://blogs.law.harvard.edu/tech/rssAn asymptotic existence result on compressed sensing matrices
http://espace.library.uq.edu.au/view/UQ:355607
2015-04-07T00:13:23Z
Bryant, Darryn; Catháin, Padraig Ó. An asymptotic solution to the cycle decomposition problem for complete graphs
http://espace.library.uq.edu.au/view/UQ:217124
2010-09-26T00:03:53Z
Bryant, Darryn; Horsley, Daniel A National Reference Station infrastructure for Australia - Using telemetry and central processing to report multi-disciplinary data streams for monitoring marine ecosystem response to climate change
http://espace.library.uq.edu.au/view/UQ:250340
As part of a broader Integrated Marine Observing System (IMOS), the marine community in Australia is developing a National Reference Station (NRS) network to monitor coastal processes. IMOS is an Australian Government initiative established under the National Collaborative Research Infrastructure Strategy (NCRIS). The aim of NCRIS is to provide researchers with access to the infrastructure and networks to build automated and ongoing in situ observing systems necessary to undertake world-class research. The NRS network fulfils this role as part of the Australian National Mooring Network, which is one of eleven IMOS facilities. The nine stations around Australia continue and expand the three existing sites where monthly water quality data have been collected since the 1940s. The overall aim of the NRS network is to provide the data to examine interactions between major coastal boundary currents and continental shelf ecosystems, especially in the context of climate change. To do this each NRS will provide long-term data series of physical and chemical parameters alongside community composition and primary (phytoplankton) and secondary (zooplankton) biological production and diversity. This will be achieved using a combination of in situ measurements (moored sensors) and monthly visits to collect samples for laboratory analysis. The NRS will provide critical baseline data to examine the impact of human stresses (such as climate change and eutrophication) on Australian marine ecosystems.2011-09-10T18:20:15Z
Lynch, T. P.; Roughan, M.; Mclaughlan, D.; Hughes, D.; Cherry, D.; Critchley, G.; Allen, S.; Pender, L.; Thompson, P.; Richardson, A. J.; Coman, F.; Steinberg, C.; Terhell, D.; Seuront, L.; Mclean, C.; Brinkman, G.; Meyers, G. A natural stochastic extension of the sandpile model on a graph
http://espace.library.uq.edu.au/view/UQ:308860
2013-09-11T16:56:35Z
Chan, Yao-ban; Marckert, Jean-François; Selig, Thomas Ancilla models for quantum operations: for what unitaries does the ancilla state have to be physical?
http://espace.library.uq.edu.au/view/UQ:299952
2013-05-12T00:48:50Z
Jiang, Zhang; Piani, Marco; Caves, Carlton M. Anderson localization and nonlinearity in flat bands
http://espace.library.uq.edu.au/view/UQ:320760
We explore the interplay between Anderson localization and Kerr nonlinearity in a lattice system containing intersecting flat and dispersive bands. The disordered system supports two distinct types of modes: high energy modes experience conventional Anderson localization. Low energy modes have a much shorter localization length, but are also highly sparse, consisting of multiple, well-separated peaks. Nonlinearity introduces different regimes of wavepacket spreading, determined by which types or modes are strongly coupled together. The spreading of localized excitations can either be massively enhanced, or suppressed, depending on the strength of nonlinearity.2014-01-14T00:26:38Z
Leykam, Daniel; Flach, Sergej; Bahat-Treidel, Omri; Desyatnikov, Anton S. A near-nhek/cft correspondence
http://espace.library.uq.edu.au/view/UQ:269827
2012-03-14T11:20:22Z
Rasmussen, Jorgen An edge-based framework for enumerating 3-manifold triangulations
http://espace.library.uq.edu.au/view/UQ:381055
A typical census of 3-manifolds contains all manifolds (under various constraints) that can be triangulated with at most n tetrahedra. Although censuses are useful resources for mathematicians, constructing them is difficult: the best algorithms to date have not gone beyond n=12. The underlying algorithms essentially (i) enumerate all relevant 4-regular multigraphs on n nodes, and then (ii) for each multigraph G they enumerate possible 3-manifold triangulations with G as their dual 1-skeleton, of which there could be exponentially many. In practice, a small number of multigraphs often dominate the running times of census algorithms: for example, in a typical census on 10 tetrahedra, almost half of the running time is spent on just 0.3% of the graphs. Here we present a new algorithm for stage (ii), which is the computational bottleneck in this process. The key idea is to build triangulations by recursively constructing neighbourhoods of edges, in contrast to traditional algorithms which recursively glue together pairs of tetrahedron faces. We implement this algorithm, and find experimentally that whilst the overall performance is mixed, the new algorithm runs significantly faster on those "pathological" multigraphs for which existing methods are extremely slow. In this way the old and new algorithms complement one another, and together can yield significant performance improvements over either method alone.2016-03-01T04:17:57Z
Burton, Benjamin A.; Pettersson, William An efficient algorithm for granular dynamics simulations with complex-shaped objects
http://espace.library.uq.edu.au/view/UQ:316034
2013-11-27T06:56:08Z
Alonso-Marroquin, Fernando; Wang, Yucang An efficient algorithm for rare-event probability estimation, combinatorial optimization, and counting
http://espace.library.uq.edu.au/view/UQ:155571
Although importance sampling is an established and effective sampling and estimation technique, it becomes unstable and unreliable for high-dimensional problems. The main reason is that the likelihood ratio in the importance sampling estimator degenerates when the dimension of the problem becomes large. Various remedies to this problem have been suggested, including heuristics such as resampling. Even so, the consensus is that for large-dimensional problems, likelihood ratios (and hence importance sampling) should be avoided. In this paper we introduce a new adaptive simulation approach that does away with likelihood ratios, while retaining the multi-level approach of the cross-entropy method. Like the latter, the method can be used for rare-event probability estimation, optimization, and counting. Moreover, the method allows one to sample exactly from the target distribution rather than asymptotically as in Markov chain Monte Carlo. Numerical examples demonstrate the effectiveness of the method for a variety of applications.2008-10-03T16:16:12Z
Botev, Z. I.; Kroese, D. P. An efficient GPU-based parallel algorithm for pricing multi-asset American options
http://espace.library.uq.edu.au/view/UQ:339901
2014-09-17T16:05:11Z
Dang, Duy-Minh; Christara, Christina C.; Jackson, Kenneth R. An efficient numerical partial differential equation approach for pricing foreign exchange interest rate hybrid derivatives
http://espace.library.uq.edu.au/view/UQ:339896
In this paper, we discuss efficient pricing methods via a partial differential equation (PDE) approach for long-dated foreign exchange (FX) interest rate hybrids under a three-factor multicurrency pricing model with FX volatility skew. The emphasis of this paper is on power-reverse dual-currency (PRDC) swaps with popular exotic features, namely knockout and FX target redemption (FX-TARN). Challenges in pricing these derivatives via a PDE approach arise from the high dimensionality of the...2014-09-17T15:29:05Z
Dang, Duy-Minh; Christara, Christina C.; Jackson, Kenneth R.; Lakhany, Asif An elliptic problem with an indefinite nonlinearity and a parameter in the boundary condition
http://espace.library.uq.edu.au/view/UQ:336973
We establish the existence of solutions of nonlinear elliptic boundary value problems involving a positive parameter on the boundary. We also examine a profile of solutions of problem (1.2) when a parameter λ tends to 0.2014-08-12T04:18:24Z
Chabrowski, Jan; Tintarev, Cyril An enduring interest in classification: supervised and unsupervised
http://espace.library.uq.edu.au/view/UQ:282476
I have researched in the field of discriminant analysis for over 40 years and for nearly as long in the field of cluster analysis. Thus, I think it is fair to say that I have had an enduring interest in discriminant and cluster analyses, that is, in classification both supervised and unsupervised. The latter terminology is used outside of statistics in fields such as artificial intelligence, machine learning, and pattern recognition. However, the gap between these fields and statistics has narrowed appreciably over the years, and discriminant analysis and cluster analysis are also often referred in statistics as supervised classification and unsupervised classification, respectively.2012-09-26T09:09:02Z
McLachlan, G. J. An Erdos-Szekeres type problem in the plane
http://espace.library.uq.edu.au/view/UQ:267828
2012-02-17T16:44:51Z
Karolyi, Gyula; Toth, G. A nested sampling algorithm for cosmological model selection
http://espace.library.uq.edu.au/view/UQ:230512
2011-02-28T09:46:18Z
Mukherjee, Pia; Parkinson, David; Liddle, Andrew R. A new algorithm for stope boundary optimization
http://espace.library.uq.edu.au/view/UQ:316266
Stopes can be simply defined as an underground opening from which ore has been excavated. Selection of the best combination of available stope boundary will directly affect the profitability of the operation. While a few attempts has been initiated to generate the optimum stope boundary for underground mining, they fail to guarantee a true optimal-ity in three-dimension block models. This paper proposed a new methodology which can find optimum stope layout for a given resource model in three-dimensions. The paper initially critically reviewed important stope boundary optimisation studies thus far, then proposed a new methodology in order to find the best stope layout for a given deposit. Subsequently it applied the proposed methodology into a block model to test its ability of producing optimum results and demonstrated its applicability in a number of different scenarios. In the last section, further analysis on strategies to find the optimum stope boundaries were demonstrated. The results prove that the proposed algorithm can find optimum stope boundaries and layouts in three-dimension for different stope sizes and stope selection strategies.2013-11-27T12:12:48Z
Topal, E.; Sens, J. A new approach to crushing 3-manifold triangulations
http://espace.library.uq.edu.au/view/UQ:381393
2016-03-05T17:28:06Z
Burton, Benjamin A. A new approach to crushing 3-manifold triangulations
http://espace.library.uq.edu.au/view/UQ:317666
2013-11-28T16:57:08Z
Burton, Benjamin A. A new approach to multiwavelength associations of astronomical sources
http://espace.library.uq.edu.au/view/UQ:230520
One of the biggest problems faced by current and next-generation astronomical surveys is trying to produce large numbers of accurate cross-identifications across a range of wavelength regimes with varying data quality and positional uncertainty. Until recently, simple spatial ‘nearest neighbour’ associations have been sufficient for most applications. However as advances in instrumentation allow more sensitive images to be made, the rapid increase in the source density has meant that source confusion across multiple wavelengths is a serious problem. The field of far-IR and sub-mm astronomy has been particularly hampered by such problems. The poor angular resolution of current sub-mm and far-IR instruments is such that in a lot of cases, there are multiple plausible counterparts for each source at other wavelengths. Here we present a new automated method of producing associations between sources at different wavelengths using a combination of spatial and spectral energy distribution information set in a Bayesian framework. Testing of the technique is performed on both simulated catalogues of sources from GaLICS and real data from multiwavelength observations of the Subaru-XMM Deep Field. It is found that a single figure of merit, the Bayes factor, can be effectively used to describe the confidence in the match. Further applications of this technique to future Herschel data sets are discussed.2011-02-28T09:47:12Z
Roseboom, Isaac G.; Oliver, Seb; Parkinson, David; Vaccari, Mattia A new approximation of relaxed energies for harmonic maps and the Faddeev model
http://espace.library.uq.edu.au/view/UQ:243288
2011-07-06T12:45:02Z
Giaquinta, Mariano; Hong, Min-Chun; Yin, Hao A new bound on the size of the largest 2-critical set in a latin square
http://espace.library.uq.edu.au/view/UQ:62496
2007-08-14T17:54:58Z
Cavenagh, N. J. A new cosmological distance measure using active galactic nuclei
http://espace.library.uq.edu.au/view/UQ:262877
2011-12-04T07:57:39Z
Watson, D.; Denney, K. D.; Vestergaard, M.; Davis, T. M. A new device-independent dimension witness and its experimental implementation
http://espace.library.uq.edu.au/view/UQ:398957
2016-08-07T00:30:21Z
Cai, Yu; Bancal, Jean-Daniel; Romero, Jacquiline; Scarani, Valerio A new diagnostic test for cross-section uncorrelatedness in nonparametric panel data models
http://espace.library.uq.edu.au/view/UQ:285192
In this paper, we propose a new diagnostic test for residual cross-section uncorrelatedness (CU) in a nonparametric panel data model. The proposed nonparametric CU test is a nonparametric counterpart of an existing parametric cross-section dependence test proposed in Pesaran (2004, Cambridge Working paper in Economics 0435). Without assuming cross-section independence, we establish asymptotic distribution for the proposed test statistic for the case where both the cross-section dimension and the time dimension go to infinity simultaneously, and then analyze the power function of the proposed test under a sequence of local alternatives that involve a nonlinear multifactor model. The simulation results and real data analysis show that the nonparametric CU test associated with an asymptotic critical value works well.2012-11-15T11:58:19Z
Chen, Jia; Gao, Jiti; Li, Degui A new diketopyrrolopyrrole-based co-polymer for ambipolar field-effect transistors and solar cells
http://espace.library.uq.edu.au/view/UQ:286241
2012-11-25T00:23:02Z
Tandy, Kristen; Dutta, Gitish K.; Zhang, Yuliang; Venkatramaiah, N.; Aljada, Muhsen; Burn, Paul L.; Meredith, Paul; Namdas, Ebinazar B.; Patil, Satish A new family of N dimensional superintegrable double singular oscillators and quadratic algebra Q(3) ⊕ so(n) ⊕ so(N-n)
http://espace.library.uq.edu.au/view/UQ:373505
2015-11-17T00:31:34Z
Hoque, Md Fazlul; Marquette, Ian; Zhang, Yao-Zhong A new method to create initially mass segregated star clusters in virial equilibrium
http://espace.library.uq.edu.au/view/UQ:265848
2012-01-24T11:50:12Z
Subr, L.; Kroupa, P.; Baumgardt, H. A new preventive maintenance strategy for items sold under warranty
http://espace.library.uq.edu.au/view/UQ:62477
When products are sold under warranty, the manufacturer incurs additional costs for warranty servicing. Preventive maintenance actions can be used to reduce this cost and these are worthwhile only if the extra cost incurred is less than the reduction achieved. In this paper we propose a new preventive maintenance policy where the parameters are selected optimally to minimize the total warranty servicing cost.2007-08-14T17:54:14Z
Jack, N.; Murthy, D. N. P. A new variational Bayesian algorithm with application to human mobility pattern modeling
http://espace.library.uq.edu.au/view/UQ:265957
2012-01-24T14:04:53Z
Wu, Burton; McGrory, Clare A.; Pettitt, Anthony N. An exact lower energy bound for the infinite square well potential
http://espace.library.uq.edu.au/view/UQ:316520
We give a lower bound for the energy of a quantum particle in the infinite square well. We show that the bound is exact and identify the well-known element that fulfils the equality. Our approach is not directly dependent on the Schrödinger equation and illustrates an example where the wavefunction is obtained directly by energy minimization. The derivation presented can serve as an example of a variational method in an undergraduate level university course in quantum mechanics.2013-11-27T17:59:51Z
Ogren, M.; Carlsson, M. An expansion tube study of high enthalpy carbon-dioxide flows
http://espace.library.uq.edu.au/view/UQ:247915
2011-09-08T23:18:55Z
McIntyre, T. J.; Eichmann, T. N.; Lourel, I.; Hajek, K. M.; Rubinsztein-Dunlop, H. An extended regression approach to estimating loads and their uncertainties in Great Barrier Reef catchments
http://espace.library.uq.edu.au/view/UQ:255074
2011-10-12T10:17:02Z
Wang, Y. G.; Kuhnert, P.; Henderson, B.; Stewart, L. An extension of the continual reassessment method using decision theory
http://espace.library.uq.edu.au/view/UQ:222301
The primary goal of a phase I trial is to find the maximally tolerated dose (MTD) of a treatment. The MTD is usually defined in terms of a tolerable probability, q* of toxicity. Our objective is to find the highest dose with toxicity risk that does not exceed q*, a criterion that is often desired in designing phase I trials. This criterion differs from that of finding the dose with toxicity risk closest to q*, that is used in methods such as the continual reassessment method. We use the theory of decision processes to find optimal sequential designs that maximize the expected number of patients within the trial allocated to the highest dose with toxicity not exceeding q*, among the doses under consideration. The proposed method is very general in the sense that criteria other than the one considered here can be optimized and that optimal dose assignment can be defined in terms of patients within or outside the trial. It includes as an important special case the continual reassessment method. Numerical study indicates the strategy compares favourably with other phase I designs.2010-11-24T13:45:47Z
Leung, Denis Heng-Yan; Wang, You-Gan An extravariation model for improving confidence intervals of population size estimates from removal data
http://espace.library.uq.edu.au/view/UQ:221254
2010-11-17T14:08:31Z
Wang, Y. G.; Loneragan, N. R. Angle structures and normal surfaces
http://espace.library.uq.edu.au/view/UQ:262686
Let M be the interior of a compact 3-manifold with boundary, and let T be an ideal triangulation of M. This paper describes necessary and sufficient conditions for the existence of angle structures, semi-angle structures and generalised angle structures on (M; T ) respectively in terms of a generalised Euler characteristic function on the solution space of the normal surface theory of (M; T ). This extends previous work of Kang and Rubinstein, and is itself generalised to a more general setting for 3-dimensional pseudo-manifolds.2011-12-01T14:28:55Z
Luo, Feng; Tillmann, Stephan Angular momentum of a strongly focused Gaussian beam
http://espace.library.uq.edu.au/view/UQ:168942
A circularly polarized paraxial Gaussian laser beam carries ±¯h angular momentum per photon as spin, with zero orbital angular momentum. Focusing the beam with a rotationally symmetric lens cannot change this angular momentum flux, yet the focused beam must have spin |Sz | < ¯h per photon. The remainder of the original spin is converted to orbital angular momentum, manifesting itself as a longitudinal optical vortex at the focus. We investigate the nature of this orbital angular momentum.2009-03-16T15:53:59Z
Nieminen, Timo A.; Stilgoe, Alexander B.; Heckenberg, Norman R.; Rubinsztein-Dunlop, Halina An Hydrophilic Anode Interlayer for Solution Processed Organohalide Perovskite Solar Cells
http://espace.library.uq.edu.au/view/UQ:372361
2015-10-30T10:58:49Z
Lin, Qianqian; Stoltzfus, Dani M.; Armin, Ardalan; Burn, Paul L.; Meredith, Paul An improved Fabens method for estimation of growth parameters in the von Bertalanffy model with individual asymptotes
http://espace.library.uq.edu.au/view/UQ:221234
2010-11-17T13:59:52Z
Wang, Y. G. An inequality relating the circumradius and diameter of two-dimensional lattice-point-free convex bodies
http://espace.library.uq.edu.au/view/UQ:303275
2013-06-20T12:24:25Z
Awyong, Poh Wah An infinite family of superintegrable systems from higher order ladder operators and supersymmetry
http://espace.library.uq.edu.au/view/UQ:259159
We discuss how we can obtain new quantum superintegrable Hamiltonians allowing the separation of variables in Cartesian coordinates with higher order integrals of motion from ladder operators. We also discuss how higher order supersymmetric quantum mechanics can be used to obtain systems with higher order ladder operators and their polynomial Heisenberg algebra. We present a new family of superintegrable systems involving the fifth Painlevé transcendent which possess fourth order ladder operators constructed from second order supersymmetric quantum mechanics. We present the polynomial algebra of this family of superintegrable systems.2011-10-24T14:21:40Z
Marquette, Ian An integrable case of the p + ip pairing Hamiltonian interacting with its environment
http://espace.library.uq.edu.au/view/UQ:379612
2016-02-14T00:19:30Z
Lukyanenko, Inna; Isaac, Phillip S.; Links, Jon An interpretation and guide to single-pass beam shaping methods using SLMs and DMDs
http://espace.library.uq.edu.au/view/UQ:396433
Exquisite manipulations of light can be performed with devices such as spatial light modulators (SLMs) and digital micromirror devices (DMDs). These devices can be used to simulate transverse paraxial beam wavefunction eigenstates such as the Hermite-Laguerre-Gaussian mode families. We investigate several beam shaping methods in terms of the wavefunctions of scattered light. Our analysis of the efficiency, behaviour and limitations of beam shaping methods is applied to both theory and experiment. The deviation from the ideal output from a valid beam shaping method is shown to be due to experimental factors which are not necessarily being accounted for. Incident beam mode shape, aberration, and the amplitude/phase transfer functions of the DMD and SLM impact the distribution of scattered light and hence the effectiveness and efficiency of a beam shaping method. Correcting for these particular details of the optical system accounts for all differences in efficiency and mode fidelity between experiment and theory. We explicitly show the impact of experimental parameter variations so that these problems may be diagnosed and corrected in an experimental beam shaping apparatus. We show that several beam shaping methods can be used for the production of beam modes in a single pass and the choice is based on the particular experimental conditions.2016-07-17T00:18:24Z
Stilgoe, Alexander B.; Kashchuk, Anatolii V.; Preece, Daryl; Rubinsztein-Dunlop, Halina An introduction to balanced sequential arrays on the square grid
http://espace.library.uq.edu.au/view/UQ:201530
2010-04-01T12:34:29Z
Street, Anne Penfold; Nester, Marks R. An introduction to effective low-energy Hamiltonians in condensed matter physics and chemistry
http://espace.library.uq.edu.au/view/UQ:268908
2012-03-05T14:19:44Z
Powell, Ben J. An introduction to quantum optomechanics
http://espace.library.uq.edu.au/view/UQ:269069
We provide an introduction to the description of mechanical systems in the quantum regime, and provide a review of the various types of micro-scale and nano-scale optomechanical and electromechanical systems. The aim is to achieve quantum control of micromechanical and nanomechanical resonators using the electromagnetic field. Such control requires the demonstration of state preparation (in particular, cooling to the ground state), coherent control and quantum-limited measurement. These problems are discussed in turn. Some particular problems in force detection, metrology, nonlinear optomechanics and many-body optomechanics are also discussed.2012-03-06T09:05:18Z
Milburn, G. J.; Woolley, M. J. An inverse theorem for the restricted set addition in Abelian groups
http://espace.library.uq.edu.au/view/UQ:268790
2012-03-02T10:48:25Z
Karolyi, G An investigation of contact transmission of methicillin resistant-Staphylococcus aureus
http://espace.library.uq.edu.au/view/UQ:70005
Hand hygiene is critical in the healthcare setting and it is believed that methicillin-resistant Staphylococcus aureus (MRSA), for example, is transmitted from patient to patient largely via the hands of health professionals. A study has been carried out at a large teaching hospital to estimate how often the gloves of a healthcare worker are contaminated with MRSA after contact with a colonized patient. The effectiveness of handwashing procedures to decontaminate the health professionals' hands was also investigated, together with how well different healthcare professional groups complied with handwashing procedures. The study showed that about 17% (9-25%) of contacts between a healthcare worker and a MRSA-colonized patient results in transmission of MRSA from a patient to the gloves of a healthcare worker. Different health professional groups have different rates of compliance with infection control procedures. Non-contact staff (cleaners, food services) had the shortest handwashing times. In this study, glove use compliance rates were 75% or above in all healthcare worker groups except doctors whose compliance was only 27%. (C) 2004 The Hospital Infection Society. Published by Elsevier Ltd. All rights reserved.2007-08-15T03:28:42Z
McBryde, E. S.; Bradley, L. C.; Whitby, M.; McElwain, D. L. S. An investigation of evaporation from single saline water droplets: experimental and theoretical approaches
http://espace.library.uq.edu.au/view/UQ:350313
2015-02-02T08:48:26Z
Sadafi, M. H.; Jahn, I.; Stilgoe, A. B.; Hooman, K. Anisotropic scattering in angular-dependent magnetoresistance oscillations of quasi-two-dimensional and quasi-one-dimensional metals: Beyond the relaxation-time approximation
http://espace.library.uq.edu.au/view/UQ:173701
The electrical resistivity for a current moving perpendicular to layers (chains) in quasi-two-dimensional (2D) [quasi-one-dimensional (1D)] metals under an applied magnetic field of varying orientation is studied using Boltzmann transport theory. We consider the simplest nontrivial quasi-2D and quasi-1D Fermi surfaces but allow for an arbitrary elastic collision integral (i.e., a scattering probability with arbitrary dependence on momentum transfer) and obtain an expression for the resistivity which generalizes that previously found using a single relaxation-time approximation. The dependence of the resistivity on the angle between the magnetic field and current changes depending on the momentum dependence of the scattering probability. So, whereas zero-field intralayer transport is sensitive only to the momentum-averaged scattering probability (the transport relaxation rate), the resistivity perpendicular to layers measured in a tilted magnetic field provides detailed information about the momentum-dependence of interlayer scattering. These results help us to clarify the meaning of the relaxation rate determined from fits of angular-dependent magnetoresistance oscillations (AMROs) experimental data to theoretical expressions. Furthermore, we suggest how AMRO might be used to probe the dominant scattering mechanism.2009-04-03T13:01:51Z
Smith, M. F.; McKenzie, R. H.